1
MHT CET 2024 9th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

If for $x \in\left(0, \frac{1}{4}\right)$, the derivative of $\tan ^{-1}\left(\frac{6 x \sqrt{x}}{1-9 x^3}\right)$ is $\sqrt{x} \cdot g(x)$, then $g(x)$ equals

A
$\frac{3 x \sqrt{x}}{1-9 x^3}$
B
$\frac{3 x}{1-9 x^3}$
C
$\frac{3}{1+9 x^3}$
D
$\frac{9}{1+9 x^3}$
2
MHT CET 2024 9th May Morning Shift
MCQ (Single Correct Answer)
+2
-0
 

Derivative of $\mathrm{e}^x$ w.r.t. $\sqrt{x}$ is

A
$\sqrt{x} \mathrm{e}^x$
B
$-2 \sqrt{x}$
C
$2 \sqrt{x} \mathrm{e}^x$
D
$ \frac{1}{2} \sqrt{x} \mathrm{e}^x$
3
MHT CET 2024 9th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

If $\mathrm{f}(x)=\frac{x^2-x}{x^2+2 x}$ then $\frac{\mathrm{d}}{\mathrm{d} x}\left(\mathrm{f}^{-1}(x)\right)$ at $x=2$ is

A
$-3$
B
3
C
$-1$
D
1
4
MHT CET 2024 4th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $y=A \cos \mathrm{n} x+\mathrm{B} \sin \mathrm{nx}$, then $\frac{\mathrm{d}^2 y}{\mathrm{~d} x^2}=$

A
$-\mathrm{n}^2 y$
B
$\mathrm{n}^2 y$
C
$\mathrm{n}^2 x$
D
$ \mathrm{n}^2 x^2$
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